We'll probably look back on this as a golden age of British electronic music, like the first days of disco, as unprepossessing producer types coax thunderous hits out of vocalists no one's heard of and live shows are euphoric, with dozens of people on stage.

Clean Bandit, friends of Disclosure and Rudimental, couldn't be more 2014 – four Cambridge graduates (two of whom met in a string quartet) operating out of a council-funded studio in Kilburn, they found some of these guest singers on a kind of music tech apprentice scheme. But if that all sounds a bit "austerity", they're marked out by their old-fashioned sense of 1980s pop entitlement – as seen in those lavish, pan-global videos (drum kits under waterfalls; Lily Cole as a mermaid) – and by their commitment to dead men's music. Mozart's House, which opens with a bit of String Quartet No 21, features words you've not heard since your Associated Board clarinet exam.

Dance music and strings have a long and fruitful history, but these days we tend to assume any orchestral bits have been cut and pasted from somewhere else. On the current single, Extraordinary, a lone cello (played by Grace Chatto) winds its way around the voice of 16-year-old Sharna Bass ("the Rihanna of south London", they call her), and you genuinely listen in a different way because you know it's real. Post-xx, there's an expectation that any self-respecting electronic band should be able to play analogue instruments, and steel pans are in rude health as far as Clean Bandit are concerned. But while the music is sophisticated – delicate meshes of digital beats, rave piano and pizzicato flourishes – the sentiments are pretty dumb: they're one of those bands that think a banal lyric repeated often enough becomes hilarious (see Telephone Banking), and though I'm inclined to agree, thousands wouldn't.

Their rubbery, eccentric image renders them a little bit smug – they look like an American Apparel ad, or an educational theatre troupe – but they're not pretentious. A&E was written while keyboard player Jack Patterson sat waiting for cellist Grace in north London's Whittington hospital. More often than not, the blend of classical and digital seems to reflect the spontaneous aural mash-ups you hear in city living – snippets of music from a car window in a traffic jam; the ting-ting-ting of a phone.

They've already had two proper top five hits, of course – Extraordinary and Rather Be, an anthem for long-distance love, which spent four weeks at No 1 in January/February. The album is too confident and colourful to disappoint those who are hoping for 10 more torch songs, running through more musical styles than your Casio keyboard on demo function. Come Over pits the Evian-pure Chatto against brrrrrrap-tastic reggae singer Stylo G. The maddest song of all is the title track, featuring Neneh Cherry-style rapper Lizzo and a male "keyboard voice" as strange as 60s TV character Torchy the Battery Boy. It'll all sound dated in a couple of years, but who cares. At its best, New Eyes is proof that you can get away with pretty much anything as long as you're clever about it. Even in its more ordinary moments, it's still a classical gas.